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#include <algorithm>
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#include <basic/math.h>
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#include <iostream>
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#include <object/object_set.h>
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#include <object/polygon.h>
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namespace are {
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Polygon::Polygon(const std::vector<Point3> &vertices, Material *material, Texture *texture) : material_(material), texture_(texture), vertices_(vertices) {
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// Initialize plane based on vertices.
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// Assumes the polygon is planar and defined by at least 3 non-collinear vertices.
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if (vertices_.size() < 3) {
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// Degenerate polygon: assign default plane to avoid undefined behavior.
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plane_.normal = Vec3(0, 1, 0);
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plane_.d = 0;
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return;
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}
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// Compute normal using the first three vertices.
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Vec3 v0 = vertices_[0];
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Vec3 v1 = vertices_[1];
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Vec3 v2 = vertices_[2];
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Vec3 u = v1 - v0;
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Vec3 v = v2 - v0;
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Vec3 n = u.cross(v);
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double len = n.length();
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if (len > GEOMETRY_EPSILON) {
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plane_.normal = n / len;
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} else {
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// Degenerate case (collinear points), try to find a valid normal or default
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plane_.normal = Vec3(0, 0, 0);
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}
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// Calculate plane constant d: N . P + d = 0 => d = -N . P
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plane_.d = -plane_.normal.dot(v0);
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}
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bool Polygon::point_in(const Point3 &point) const {
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if (vertices_.size() < 3) {
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return false;
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}
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// Step 1: Check if the point lies on the polygon's plane.
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double dist = plane_.normal.dot(point) + plane_.d;
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if (std::fabs(dist) > GEOMETRY_EPSILON) {
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return false;
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}
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// Step 2: Check if the point is within the polygon boundaries.
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// Using the same-side method for convex polygons.
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// The point must be on the same side of all edges defined by the polygon vertices.
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Vec3 n = plane_.normal;
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int n_verts = vertices_.size();
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// Determine the expected sign of the cross product relative to the normal.
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// We check the first edge to establish the reference side (or check all against the normal).
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// Robust approach: Check that all cross products have the same sign (positive or negative) relative to N.
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bool sign_determined = false;
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bool positive_side = false;
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for (int i = 0; i < n_verts; ++i) {
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const Point3 &curr = vertices_[i];
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const Point3 &next = vertices_[(i + 1) % n_verts];
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// Edge vector
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Vec3 edge = next - curr;
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// Vector from vertex to point
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Vec3 vec_to_p = point - curr;
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// Cross product: edge x vec_to_p.
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// The direction of this vector indicates which side of the edge the point is on.
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Vec3 cross_prod = edge.cross(vec_to_p);
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// Dot product with polygon normal to get signed distance (scaled)
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double dot_val = cross_prod.dot(n);
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// If the point is exactly on the edge (within epsilon), the dot_val is close to 0.
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// Otherwise, we check consistency of the sign.
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if (std::fabs(dot_val) > GEOMETRY_EPSILON) {
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if (!sign_determined) {
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sign_determined = true;
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positive_side = (dot_val > 0);
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} else {
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// If the current sign differs from the reference sign, point is outside.
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if ((dot_val > 0) != positive_side) {
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return false;
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}
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}
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}
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}
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return true;
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}
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bool Polygon::intersect_ray(const Ray &ray, Point3 &hit_point) const {
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// Step 1: Intersect ray with the infinite plane.
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// Plane equation: N . P + d = 0
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// Ray equation: P(t) = Q + t * D
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// Substitute: N . (Q + t * D) + d = 0
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// Solve for t: t = -(N . Q + d) / (N . D)
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double denom = plane_.normal.dot(ray.D);
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// Check if ray is parallel to the plane.
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if (std::fabs(denom) < GEOMETRY_EPSILON) {
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return false;
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}
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double t = -(plane_.normal.dot(ray.Q) + plane_.d) / denom;
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// Check if intersection is behind the ray origin.
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if (t < GEOMETRY_EPSILON) {
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return false;
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}
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// Calculate the candidate intersection point.
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Point3 candidate_point = ray.Q + t * ray.D;
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// Step 2: Check if the intersection point lies inside the polygon boundaries.
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if (point_in(candidate_point)) {
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hit_point = candidate_point;
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return true;
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}
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return false;
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}
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static int diguicishu = 0;
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Texture Polygon::trace_texture(const ObjectSet &object_set, const Point3 &viewport_origin_point) const {
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// 1. 拷贝当前纹理的副本作为返回值
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Texture result(texture_->width_, texture_->height_, Color3(0, 0, 0));
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for (int y = 0; y < texture_->height_; ++y) {
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for (int x = 0; x < texture_->width_; ++x) {
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result.pixel(x, y) = texture_->pixel(x, y);
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}
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}
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// 2. 检测当前纹理是否需要处理反射
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Point3 dummy_new_origin;
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if (!material_->reflect(plane_, viewport_origin_point, dummy_new_origin) || ++diguicishu >= 10) {
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// 不需要处理反射，直接返回拷贝的副本
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return result;
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}
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// 3. 建立当前Polygon平面的局部2D坐标系
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Vec3 normal = plane_.normal.normalized();
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// 选择两个正交的基向量 u_axis 和 v_axis
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Vec3 u_axis, v_axis;
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if (std::abs(normal.x()) < 0.9) {
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u_axis = normal.cross(Vec3(1, 0, 0)).normalized();
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} else {
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u_axis = normal.cross(Vec3(0, 1, 0)).normalized();
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}
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v_axis = normal.cross(u_axis).normalized();
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// 计算当前polygon顶点在平面坐标系中的UV边界（最小包围盒）
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Point3 plane_origin = vertices_[0];
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double min_u_self = std::numeric_limits<double>::max();
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double max_u_self = std::numeric_limits<double>::lowest();
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double min_v_self = std::numeric_limits<double>::max();
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double max_v_self = std::numeric_limits<double>::lowest();
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std::vector<std::pair<double, double>> self_uvs;
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for (const auto &vertex : vertices_) {
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Vec3 rel = vertex - plane_origin;
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double u = rel.dot(u_axis);
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double v = rel.dot(v_axis);
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self_uvs.push_back({ u, v });
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min_u_self = std::min(min_u_self, u);
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max_u_self = std::max(max_u_self, u);
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min_v_self = std::min(min_v_self, v);
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max_v_self = std::max(max_v_self, v);
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}
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double width_self = max_u_self - min_u_self;
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double height_self = max_v_self - min_v_self;
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// 4. 构建视锥体边界平面（由viewport_origin_point和当前polygon的边组成）
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std::vector<Plane> frustum_planes;
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int n_verts = static_cast<int>(vertices_.size());
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// 计算当前polygon的中心点
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Point3 self_centroid(0, 0, 0);
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for (const auto &v : vertices_) {
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self_centroid += v;
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}
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self_centroid = self_centroid / static_cast<double>(n_verts);
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for (int i = 0; i < n_verts; ++i) {
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const Point3 &v1 = vertices_[i];
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const Point3 &v2 = vertices_[(i + 1) % n_verts];
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// 构建由viewport_origin_point, v1, v2三点确定的平面
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Vec3 edge = v2 - v1;
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Vec3 to_v1 = v1 - viewport_origin_point;
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Vec3 frustum_normal = edge.cross(to_v1);
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if (frustum_normal.near_zero()) {
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continue; // 退化情况，跳过
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}
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frustum_normal.normalize();
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// 确保法向量指向视锥体内部（朝向polygon中心）
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Vec3 to_centroid = self_centroid - viewport_origin_point;
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if (frustum_normal.dot(to_centroid) < 0) {
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frustum_normal = -frustum_normal;
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}
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frustum_planes.push_back(Plane(viewport_origin_point, frustum_normal));
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}
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// 添加viewport平面本身（确保物体在viewport的正面）
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Vec3 view_dir = (self_centroid - viewport_origin_point).normalized();
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Plane near_plane(viewport_origin_point, view_dir);
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// 5. 遍历object_set，找出与视锥体相交的polygon
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struct PolygonDistance {
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Polygon *polygon;
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double distance;
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Point3 centroid;
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};
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std::vector<PolygonDistance> intersected_polygons;
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for (Polygon *obj : object_set.object_set) {
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// 跳过自身
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if (obj == this) {
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continue;
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}
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// 计算目标polygon的重心
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Point3 target_centroid(0, 0, 0);
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int target_n = static_cast<int>(obj->vertices_.size());
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for (const auto &v : obj->vertices_) {
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target_centroid += v;
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}
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target_centroid = target_centroid / static_cast<double>(target_n);
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// 检测目标polygon是否与视锥体相交
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bool intersects = false;
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for (const Point3 &vertex : vertices_) { // 检查原点到当前polygon顶点的射线是否与目标polygon相交
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Vec3 direction = vertex - viewport_origin_point;
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if(direction.near_zero()) {
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continue;
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}
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Ray ray(viewport_origin_point, direction);
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Point3 hit;
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// std::cout << "Checking hit: " << vertices_.size() << std::endl;
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// 视锥体原点到viewport当前端点的连线与目标polugon相交
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if(obj->intersect_ray(ray, hit)) {
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// std::cout << "HIT!" << std::endl;
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// 检测hit_point是否在viewport前面
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double dist_to_hit = (hit - viewport_origin_point).length();
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double dist_to_vertex = (vertex - viewport_origin_point).length();
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if(dist_to_hit > dist_to_vertex - GEOMETRY_EPSILON) {
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intersects = true;
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break;
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}
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}
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}
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if (!intersects) { // 如果顶点都不在内部，检查从viewport_origin_point到目标顶点的射线是否与当前polygon相交
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for (const Point3 &vertex : obj->vertices_) {
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Vec3 dir = vertex - viewport_origin_point;
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if (dir.near_zero())
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continue;
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dir.normalize();
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Ray ray(viewport_origin_point, dir);
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Point3 hit;
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if (intersect_ray(ray, hit)) {
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// 确保目标顶点在hit点之后（相对于viewport_origin_point）
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double dist_to_hit = (hit - viewport_origin_point).length();
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double dist_to_vertex = (vertex - viewport_origin_point).length();
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if (dist_to_vertex > dist_to_hit - GEOMETRY_EPSILON) {
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intersects = true;
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break;
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}
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}
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}
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}
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if (!intersects) { // 检查目标polygon的边是否穿过视锥体
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for (int i = 0; i < target_n && !intersects; ++i) {
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const Point3 &edge_start = obj->vertices_[i];
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const Point3 &edge_end = obj->vertices_[(i + 1) % target_n];
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Vec3 edge_dir = edge_end - edge_start;
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double edge_len = edge_dir.length();
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if (edge_len < GEOMETRY_EPSILON)
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continue;
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edge_dir = edge_dir / edge_len;
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Ray edge_ray(edge_start, edge_dir);
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Point3 plane_hit;
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if (plane_.intersect_ray(edge_ray, plane_hit)) {
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double t = (plane_hit - edge_start).dot(edge_dir);
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if (t > GEOMETRY_EPSILON && t < edge_len - GEOMETRY_EPSILON) {
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// 交点在边上，检查是否在当前polygon内
|
|
|
|
|
if (point_in(plane_hit)) {
|
|
|
|
|
intersects = true;
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
if (intersects) {
|
|
|
|
|
double dist = (target_centroid - viewport_origin_point).length();
|
|
|
|
|
intersected_polygons.push_back({ obj, dist, target_centroid });
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
std::cout << "Hitted" << intersected_polygons.size() << " polygons." << std::endl;
|
|
|
|
|
|
|
|
|
|
// 6. 按距离降序排序（远的先绘制，近的后绘制覆盖）
|
|
|
|
|
std::sort(intersected_polygons.begin(), intersected_polygons.end(),
|
|
|
|
|
[](const PolygonDistance &a, const PolygonDistance &b) {
|
|
|
|
|
return a.distance > b.distance;
|
|
|
|
|
});
|
|
|
|
|
|
|
|
|
|
int i = 0;
|
|
|
|
|
// 7. 遍历排序后的polygon数组，进行纹理映射
|
|
|
|
|
for (const auto &pd : intersected_polygons) {
|
|
|
|
|
Polygon *target_polygon = pd.polygon;
|
|
|
|
|
|
|
|
|
|
// 计算目标polygon每个顶点投影到当前平面的UV坐标
|
|
|
|
|
std::vector<std::pair<double, double>> projected_uvs;
|
|
|
|
|
bool projection_valid = true;
|
|
|
|
|
|
|
|
|
|
for (const Point3 &vertex : target_polygon->vertices_) {
|
|
|
|
|
Vec3 dir = vertex - viewport_origin_point;
|
|
|
|
|
if (dir.near_zero()) {
|
|
|
|
|
projection_valid = false;
|
|
|
|
|
break;
|
|
|
|
|
}
|
|
|
|
|
dir.normalize();
|
|
|
|
|
|
|
|
|
|
Ray ray(viewport_origin_point, dir);
|
|
|
|
|
Point3 intersection;
|
|
|
|
|
if (!plane_.intersect_ray(ray, intersection)) {
|
|
|
|
|
projection_valid = false;
|
|
|
|
|
break;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
// 检查交点是否在viewport_origin_point和顶点之间的正确方向
|
|
|
|
|
Vec3 to_intersection = intersection - viewport_origin_point;
|
|
|
|
|
Vec3 to_vertex = vertex - viewport_origin_point;
|
|
|
|
|
if (to_intersection.dot(to_vertex) < GEOMETRY_EPSILON) {
|
|
|
|
|
projection_valid = false;
|
|
|
|
|
break;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
// 计算交点的2D UV坐标
|
|
|
|
|
Vec3 rel = intersection - plane_origin;
|
|
|
|
|
double u = rel.dot(u_axis);
|
|
|
|
|
double v = rel.dot(v_axis);
|
|
|
|
|
projected_uvs.push_back({ u, v });
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
if (!projection_valid || projected_uvs.size() != target_polygon->vertices_.size()) {
|
|
|
|
|
continue;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
// 获取反射后的viewport origin（用于递归调用）
|
|
|
|
|
Point3 reflected_origin;
|
|
|
|
|
if (!material_->reflect(target_polygon->plane_, viewport_origin_point, reflected_origin)) {
|
|
|
|
|
continue;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
// 递归获取目标polygon的纹理
|
|
|
|
|
Texture target_texture = target_polygon->trace_texture(object_set, reflected_origin);
|
|
|
|
|
// target_texture.save_texture(std::to_string(diguicishu) + "_" + std::to_string(i++) + ".ppm");
|
|
|
|
|
|
|
|
|
|
// 计算目标polygon顶点在其自身纹理中的UV坐标（最小包围盒原则）
|
|
|
|
|
Vec3 target_normal = target_polygon->plane_.normal.normalized();
|
|
|
|
|
Vec3 target_u_axis, target_v_axis;
|
|
|
|
|
if (std::abs(target_normal.x()) < 0.9) {
|
|
|
|
|
target_u_axis = target_normal.cross(Vec3(1, 0, 0)).normalized();
|
|
|
|
|
} else {
|
|
|
|
|
target_u_axis = target_normal.cross(Vec3(0, 1, 0)).normalized();
|
|
|
|
|
}
|
|
|
|
|
target_v_axis = target_normal.cross(target_u_axis).normalized();
|
|
|
|
|
|
|
|
|
|
Point3 target_plane_origin = target_polygon->vertices_[0];
|
|
|
|
|
double target_min_u = std::numeric_limits<double>::max();
|
|
|
|
|
double target_max_u = std::numeric_limits<double>::lowest();
|
|
|
|
|
double target_min_v = std::numeric_limits<double>::max();
|
|
|
|
|
double target_max_v = std::numeric_limits<double>::lowest();
|
|
|
|
|
|
|
|
|
|
std::vector<std::pair<double, double>> target_local_uvs;
|
|
|
|
|
for (const auto &vertex : target_polygon->vertices_) {
|
|
|
|
|
Vec3 rel = vertex - target_plane_origin;
|
|
|
|
|
double u = rel.dot(target_u_axis);
|
|
|
|
|
double v = rel.dot(target_v_axis);
|
|
|
|
|
target_local_uvs.push_back({ u, v });
|
|
|
|
|
target_min_u = std::min(target_min_u, u);
|
|
|
|
|
target_max_u = std::max(target_max_u, u);
|
|
|
|
|
target_min_v = std::min(target_min_v, v);
|
|
|
|
|
target_max_v = std::max(target_max_v, v);
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
double target_width = target_max_u - target_min_u;
|
|
|
|
|
double target_height = target_max_v - target_min_v;
|
|
|
|
|
|
|
|
|
|
if (target_width < GEOMETRY_EPSILON || target_height < GEOMETRY_EPSILON) {
|
|
|
|
|
continue;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
// 将目标polygon的局部UV转换为纹理坐标（0到1范围，然后映射到像素）
|
|
|
|
|
std::vector<std::pair<double, double>> target_tex_coords;
|
|
|
|
|
for (const auto &uv : target_local_uvs) {
|
|
|
|
|
double tex_u = (uv.first - target_min_u) / target_width;
|
|
|
|
|
double tex_v = (uv.second - target_min_v) / target_height;
|
|
|
|
|
target_tex_coords.push_back({ tex_u, tex_v });
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
// 计算投影多边形的边界框
|
|
|
|
|
double proj_min_u = std::numeric_limits<double>::max();
|
|
|
|
|
double proj_max_u = std::numeric_limits<double>::lowest();
|
|
|
|
|
double proj_min_v = std::numeric_limits<double>::max();
|
|
|
|
|
double proj_max_v = std::numeric_limits<double>::lowest();
|
|
|
|
|
for (const auto &uv : projected_uvs) {
|
|
|
|
|
proj_min_u = std::min(proj_min_u, uv.first);
|
|
|
|
|
proj_max_u = std::max(proj_max_u, uv.first);
|
|
|
|
|
proj_min_v = std::min(proj_min_v, uv.second);
|
|
|
|
|
proj_max_v = std::max(proj_max_v, uv.second);
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
// 裁剪到当前polygon的UV范围
|
|
|
|
|
proj_min_u = std::max(proj_min_u, min_u_self);
|
|
|
|
|
proj_max_u = std::min(proj_max_u, max_u_self);
|
|
|
|
|
proj_min_v = std::max(proj_min_v, min_v_self);
|
|
|
|
|
proj_max_v = std::min(proj_max_v, max_v_self);
|
|
|
|
|
|
|
|
|
|
if (proj_min_u >= proj_max_u || proj_min_v >= proj_max_v) {
|
|
|
|
|
continue;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
// 遍历结果纹理的每个像素，进行逆映射
|
|
|
|
|
for (int py = 0; py < result.height_; ++py) {
|
|
|
|
|
for (int px = 0; px < result.width_; ++px) {
|
|
|
|
|
// 将像素坐标转换为当前polygon平面的UV坐标
|
|
|
|
|
double uv_u = min_u_self + (static_cast<double>(px) + 0.5) / result.width_ * width_self;
|
|
|
|
|
double uv_v = min_v_self + (static_cast<double>(py) + 0.5) / result.height_ * height_self;
|
|
|
|
|
|
|
|
|
|
// 检查该点是否在投影多边形内（使用重心坐标或射线法）
|
|
|
|
|
// 使用射线法检测点是否在多边形内
|
|
|
|
|
bool inside_projected = false;
|
|
|
|
|
int num_projected = static_cast<int>(projected_uvs.size());
|
|
|
|
|
int crossings = 0;
|
|
|
|
|
for (int i = 0; i < num_projected; ++i) {
|
|
|
|
|
const auto &p1 = projected_uvs[i];
|
|
|
|
|
const auto &p2 = projected_uvs[(i + 1) % num_projected];
|
|
|
|
|
|
|
|
|
|
if ((p1.second <= uv_v && p2.second > uv_v) || (p2.second <= uv_v && p1.second > uv_v)) {
|
|
|
|
|
double t = (uv_v - p1.second) / (p2.second - p1.second);
|
|
|
|
|
double x_intersect = p1.first + t * (p2.first - p1.first);
|
|
|
|
|
if (uv_u < x_intersect) {
|
|
|
|
|
crossings++;
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
inside_projected = (crossings % 2) == 1;
|
|
|
|
|
|
|
|
|
|
if (!inside_projected) {
|
|
|
|
|
continue;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
// 检查是否在当前polygon内
|
|
|
|
|
Point3 world_point = plane_origin + uv_u * u_axis + uv_v * v_axis;
|
|
|
|
|
if (!point_in(world_point)) {
|
|
|
|
|
continue;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
// 使用重心坐标进行纹理映射（适用于任意凸多边形）
|
|
|
|
|
// 对于三角形，使用重心坐标；对于其他多边形，使用广义重心坐标
|
|
|
|
|
|
|
|
|
|
// 计算广义重心坐标（Mean Value Coordinates）
|
|
|
|
|
std::vector<double> weights(num_projected, 0.0);
|
|
|
|
|
double weight_sum = 0.0;
|
|
|
|
|
bool on_vertex = false;
|
|
|
|
|
int vertex_idx = -1;
|
|
|
|
|
bool on_edge = false;
|
|
|
|
|
int edge_idx = -1;
|
|
|
|
|
double edge_t = 0.0;
|
|
|
|
|
|
|
|
|
|
for (int i = 0; i < num_projected; ++i) {
|
|
|
|
|
double dx = projected_uvs[i].first - uv_u;
|
|
|
|
|
double dy = projected_uvs[i].second - uv_v;
|
|
|
|
|
double dist = std::sqrt(dx * dx + dy * dy);
|
|
|
|
|
if (dist < GEOMETRY_EPSILON) {
|
|
|
|
|
on_vertex = true;
|
|
|
|
|
vertex_idx = i;
|
|
|
|
|
break;
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
if (on_vertex) {
|
|
|
|
|
// 点在顶点上
|
|
|
|
|
double tex_x = target_tex_coords[vertex_idx].first * (target_texture.width_ - 1);
|
|
|
|
|
double tex_y = target_tex_coords[vertex_idx].second * (target_texture.height_ - 1);
|
|
|
|
|
int src_x = std::clamp(static_cast<int>(tex_x + 0.5), 0, target_texture.width_ - 1);
|
|
|
|
|
int src_y = std::clamp(static_cast<int>(tex_y + 0.5), 0, target_texture.height_ - 1);
|
|
|
|
|
result.pixel(px, py) = target_texture.pixel(src_x, src_y);
|
|
|
|
|
continue;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
// 检查是否在边上
|
|
|
|
|
for (int i = 0; i < num_projected && !on_edge; ++i) {
|
|
|
|
|
const auto &p1 = projected_uvs[i];
|
|
|
|
|
const auto &p2 = projected_uvs[(i + 1) % num_projected];
|
|
|
|
|
|
|
|
|
|
double edge_dx = p2.first - p1.first;
|
|
|
|
|
double edge_dy = p2.second - p1.second;
|
|
|
|
|
double edge_len_sq = edge_dx * edge_dx + edge_dy * edge_dy;
|
|
|
|
|
|
|
|
|
|
if (edge_len_sq < GEOMETRY_EPSILON * GEOMETRY_EPSILON)
|
|
|
|
|
continue;
|
|
|
|
|
|
|
|
|
|
double t = ((uv_u - p1.first) * edge_dx + (uv_v - p1.second) * edge_dy) / edge_len_sq;
|
|
|
|
|
if (t < 0.0 || t > 1.0)
|
|
|
|
|
continue;
|
|
|
|
|
|
|
|
|
|
double closest_x = p1.first + t * edge_dx;
|
|
|
|
|
double closest_y = p1.second + t * edge_dy;
|
|
|
|
|
double dist_to_edge = std::sqrt((uv_u - closest_x) * (uv_u - closest_x) + (uv_v - closest_y) * (uv_v - closest_y));
|
|
|
|
|
|
|
|
|
|
if (dist_to_edge < GEOMETRY_EPSILON) {
|
|
|
|
|
on_edge = true;
|
|
|
|
|
edge_idx = i;
|
|
|
|
|
edge_t = t;
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
if (on_edge) {
|
|
|
|
|
// 点在边上，线性插值
|
|
|
|
|
int i1 = edge_idx;
|
|
|
|
|
int i2 = (edge_idx + 1) % num_projected;
|
|
|
|
|
double tex_u_interp = target_tex_coords[i1].first * (1.0 - edge_t) + target_tex_coords[i2].first * edge_t;
|
|
|
|
|
double tex_v_interp = target_tex_coords[i1].second * (1.0 - edge_t) + target_tex_coords[i2].second * edge_t;
|
|
|
|
|
|
|
|
|
|
double tex_x = tex_u_interp * (target_texture.width_ - 1);
|
|
|
|
|
double tex_y = tex_v_interp * (target_texture.height_ - 1);
|
|
|
|
|
int src_x = std::clamp(static_cast<int>(tex_x + 0.5), 0, target_texture.width_ - 1);
|
|
|
|
|
int src_y = std::clamp(static_cast<int>(tex_y + 0.5), 0, target_texture.height_ - 1);
|
|
|
|
|
result.pixel(px, py) = target_texture.pixel(src_x, src_y);
|
|
|
|
|
continue;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
// 使用Mean Value Coordinates计算广义重心坐标
|
|
|
|
|
for (int i = 0; i < num_projected; ++i) {
|
|
|
|
|
int prev = (i - 1 + num_projected) % num_projected;
|
|
|
|
|
int next = (i + 1) % num_projected;
|
|
|
|
|
|
|
|
|
|
double dx_i = projected_uvs[i].first - uv_u;
|
|
|
|
|
double dy_i = projected_uvs[i].second - uv_v;
|
|
|
|
|
double r_i = std::sqrt(dx_i * dx_i + dy_i * dy_i);
|
|
|
|
|
|
|
|
|
|
double dx_prev = projected_uvs[prev].first - uv_u;
|
|
|
|
|
double dy_prev = projected_uvs[prev].second - uv_v;
|
|
|
|
|
double r_prev = std::sqrt(dx_prev * dx_prev + dy_prev * dy_prev);
|
|
|
|
|
|
|
|
|
|
double dx_next = projected_uvs[next].first - uv_u;
|
|
|
|
|
double dy_next = projected_uvs[next].second - uv_v;
|
|
|
|
|
double r_next = std::sqrt(dx_next * dx_next + dy_next * dy_next);
|
|
|
|
|
|
|
|
|
|
// 计算角度
|
|
|
|
|
auto compute_tan_half_angle = [](double dx1, double dy1, double r1,
|
|
|
|
|
double dx2, double dy2, double r2) -> double {
|
|
|
|
|
double dot = dx1 * dx2 + dy1 * dy2;
|
|
|
|
|
double cross = dx1 * dy2 - dy1 * dx2;
|
|
|
|
|
double cos_angle = dot / (r1 * r2);
|
|
|
|
|
cos_angle = std::clamp(cos_angle, -1.0, 1.0);
|
|
|
|
|
double sin_angle = cross / (r1 * r2);
|
|
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// tan(angle/2) = sin(angle) / (1 + cos(angle))
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double denom = 1.0 + cos_angle;
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if (std::abs(denom) < GEOMETRY_EPSILON) {
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return (sin_angle >= 0) ? 1e10 : -1e10;
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}
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return sin_angle / denom;
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};
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double tan_alpha_prev = compute_tan_half_angle(dx_prev, dy_prev, r_prev, dx_i, dy_i, r_i);
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double tan_alpha_next = compute_tan_half_angle(dx_i, dy_i, r_i, dx_next, dy_next, r_next);
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weights[i] = (tan_alpha_prev + tan_alpha_next) / r_i;
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weight_sum += weights[i];
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}
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|
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if (std::abs(weight_sum) < GEOMETRY_EPSILON) {
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|
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|
|
continue;
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}
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// 归一化权重并计算插值纹理坐标
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|
|
|
|
double interp_tex_u = 0.0;
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|
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|
|
double interp_tex_v = 0.0;
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|
|
|
|
for (int i = 0; i < num_projected; ++i) {
|
|
|
|
|
double normalized_weight = weights[i] / weight_sum;
|
|
|
|
|
interp_tex_u += normalized_weight * target_tex_coords[i].first;
|
|
|
|
|
interp_tex_v += normalized_weight * target_tex_coords[i].second;
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|
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|
}
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|
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|
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|
|
|
|
// 将归一化纹理坐标转换为像素坐标
|
|
|
|
|
double tex_x = interp_tex_u * (target_texture.width_ - 1);
|
|
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|
|
double tex_y = interp_tex_v * (target_texture.height_ - 1);
|
|
|
|
|
|
|
|
|
|
// 双线性插值采样
|
|
|
|
|
int x0 = static_cast<int>(std::floor(tex_x));
|
|
|
|
|
int y0 = static_cast<int>(std::floor(tex_y));
|
|
|
|
|
int x1 = x0 + 1;
|
|
|
|
|
int y1 = y0 + 1;
|
|
|
|
|
|
|
|
|
|
x0 = std::clamp(x0, 0, target_texture.width_ - 1);
|
|
|
|
|
x1 = std::clamp(x1, 0, target_texture.width_ - 1);
|
|
|
|
|
y0 = std::clamp(y0, 0, target_texture.height_ - 1);
|
|
|
|
|
y1 = std::clamp(y1, 0, target_texture.height_ - 1);
|
|
|
|
|
|
|
|
|
|
double fx = tex_x - std::floor(tex_x);
|
|
|
|
|
double fy = tex_y - std::floor(tex_y);
|
|
|
|
|
|
|
|
|
|
Color3 c00 = target_texture.pixel(x0, y0);
|
|
|
|
|
Color3 c10 = target_texture.pixel(x1, y0);
|
|
|
|
|
Color3 c01 = target_texture.pixel(x0, y1);
|
|
|
|
|
Color3 c11 = target_texture.pixel(x1, y1);
|
|
|
|
|
|
|
|
|
|
Color3 sampled_color = c00 * (1.0 - fx) * (1.0 - fy) + c10 * fx * (1.0 - fy) + c01 * (1.0 - fx) * fy + c11 * fx * fy;
|
|
|
|
|
|
|
|
|
|
// 将采样的颜色写入结果纹理（金属反射直接覆盖）
|
|
|
|
|
result.pixel(px, py) = sampled_color;
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
return result;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
}
|
